A manufacturing firm has signed a contract to produce a product to demand, receiving $500 per unit. The firm could either produce the product itself or outsource the production. Demand is exponentially distributed with a mean of 10,000 units per year. In-house production has normally-distributed fixed costs with mean of $500,000 and a standard deviation of $100,000 and normally-distributed variable costs with mean $200 and standard deviation of $10. Outsourcing has no fixed cost, but variable costs are $250.

a. Create a diagram for this problem

b. Forecast the profit for each alternative

c. Determine the difference in profit

d. Determine the probability that each alternative achieves at least $0 profit, $100,000 profit, and $200,000 profit